1. Field of the Invention
This invention relates generally to geodesic dome-like structures including interconnected triangular panels and, more particularly, to such structures whose panels are pivotally interconnected during assembly.
2. Description of the Prior Art
Geodesic dome structures are polygonal bodies whose sides are so numerous that they appear spherical or partially spherical in shape. Such structure can be generated by starting with a regular icosahedron and a sphere whose surface passes through the apices of the icosahedron. A regular icosahedron is a polyhedron having twenty identical faces in the form of equilateral triangles. These triangular faces are then subdivided in various ways and vertices of these subdivided portions are then projected outwardly in a radial direction with respect to the sphere to its surface at various points. The points are then connected by straight lines to form polygons and a plane through the interconnected straight lines of each polygon then forms the outer face of the geodesic dome. Such a dome structure so generated is generally spherical in shape.
Although there are many ways to subdivide the faces of an icosahedron to generate a geodesic dome, high strength dome structures are provided when the outer faces of the dome are in the form of triangles that are substantially equilateral. Two methods by which geodesic domes can be formed with substantially equilateral triangular faces are referred to as the "triacon" breakdown and the "alternate" breakdown. The number of faces formed on the resultant geodesic dome with either of these methods, as well as with other types of breakdowns, depends on the "frequency" of the breakdown. Generally, the frequency is normally on the order of two, three, or four and defines the number of times the icosahedron faces are subdivided before the vertices are projected outwardly to the surface of the sphere.
In the "triacon" breakdown, the angles of the icosahedron faces at their vertices are bisected and the intersection of the three lines so generated forms a point which is connected with each of the vertices by lines of equal length. Using this point as the center and the length of these three lines, six equilateral triangles are then generated about the point. Consequently, there is an overlapping of the triangles formed from adjacent faces of the icosahedron. At this stage, projecting the vertices of the triangles formed outwardly in a radial direction to the sphere surface would form the points necessary to generate geodesic dome faces for a two frequency dome. The triangles can be further subdivided in the same manner and then projected outwardly to the sphere surface to form faces for other even number frequency domes, however, odd number frequency domes with this breakdown are not possible.
In the "alternate" breakdown, points are located along the sides of the triangular icosahedron faces so as to divide these sides into a number of portions of equal length in accordance with the frequency to be utilized. One point at the midpoint of the triangular sides is utilized to provide two equal length portions for a two frequency dome, while two points are utilized to provide three equal length portions for a three frequency dome, etc. Lines are then drawn through these points parallel to the sides of the icosahedron faces so as to divide the faces into a plurality of triangles, the number of which depends upon the frequency. For an alternate breakdown of two frequency, four triangles will be defined while nine will be defined for a three frequency breakdown and sixteen will be defined for a four frequency breakdown. Since the sides of the triangles formed by this subdividing are located at various distances from the triangular icosahedron face vertices, and likewise in their triacon breakdown, projection of the points defining their vertices out to the sphere that encompasses the icosahedron does not result in the formation of completely equilateral triangles whose sides are all precisely equal to each other. Rather, the points furthest from the vertices are located inward from the sphere surface a greater distance than those closer to the vertices and, consequently, outward projection of the points to the sphere surfaces causes them to intersect with the sphere surface at locations spaced from each other varying distances. The points closer to the icosahedron face vertices will intersect with the sphere at locations slightly closer to each other than the points further from the vertices. Connection of the locations of intersection then generates triangular dome faces that are close to being equilateral but not precisely of this shape. For a two frequency alternate breakdown, the triangular faces of the dome generated are of isosceles shape with their longer and shorter sides having lengths within fifteen percent of each other so as to be close to being equilateral. Likewise, for a three or four frequency dome, each isosceles triangular face of the dome has longer and shorter sides whose lengths are also within approximately fifteen percent of each other.
The now expired patent of Richard Buckminster Fuller, 2,682,235 discloses the original geodesic dome type structure to which this invention relates. Other geodesic dome-like structures are shown by subsequent Fuller U.S. Pat. Nos. listed as follows: 2,914,074; 3,197,927; and 3,206,144.
To construct a geodesic dome from struts that extend along the sides of the dome faces and have opposite ends connected to each other, interconnection of the struts to assemble the dome is somewhat complicated by the fact that compound angles are necessary in order to engage the strut ends with each other for securement. Reference should be made to the U.S. Pat. of Miller No. 3,114,176 for a more complete understanding of this problem. Triangular dome panels utilized to form a dome structure or the like have in the past been pivotally interconnected to eliminate the problem caused by the compound angles necessary to engage strut ends with each other to form a rigid structure. This type of pivotal interconnection is shown by the following U.S. Pat. Nos.: 3,343,324; 3,640,034; and 3,921,349.
Other geodesic domes and related structures are disclosed by the following U.S. Pat. Nos.: 3,077,702; 3,341,989; 3,362,127; 3,871,143; and 3,909,994.